Problem: Complete the recursive formula of the geometric sequence $-0.6\,,\,3\,,-15\,,\,75,...$. $c(1)=$
Solution: The first term is $-0.6$ and the common ratio is $-5$. ${\times (-5)\,\curvearrowright}$ ${\times (-5)\,\curvearrowright}$ ${\times (-5)\,\curvearrowright}$ $-0.6,$ $3,$ $-15,$ $75,...$ This is the recursive formula of $-0.6\,,\,3\,,-15\,,\,75,...$. $\begin{cases} c(1)=-0.6 \\\\ c(n)=c(n-1)\cdot(-5) \end{cases}$